Cool. I'm a visual learner. I understand how it works, but I can't really explain it. Fundamentally, there's really no difference in doing it the long hand way vs. graphically. I didn't know this technique existed, I'll try to use it from now on.

My lame attempt to explain this. For example we need to calculate 12 x 14 = I broke it down to (10 + 2) x (10 + 4) = 100 + (20 + 40) + 8 Draw the lines according to the method, you'll see that the number of points in each region corresponds to the broken down equation I did above: a. 2 lines intersect makes 1 point, since these 2 lines represent the first digit (1) of the 12 and 14 number, they correspond to 10 x 10, put the number of points down as the first digit of your result b. 4 lines intersect 1 line makes 4 points, since these 4 lines represent the second digit (4) of the number 14, they correspond to 10 x 4 c. 2 lines intersect 1 line makes 2 points, since these 2 lines represent the second digit (2) of the number 12, they correspond to 10 x 2 + add both the number of points found in b. and c. to get the second digit of your result d. 2 lines intersect 4 lines makes 8 points, just like 2 x 4, since these 2 lines and 4 lines both represent the second digits of number 12 and 14 respectively, they correspond to 2 x 4 write down the number of points found in d. as the last digit of your result. The key to this method is line intersection, x number of parallel lines intersect at a right angle with y number of parallel lines gives us a total of x * y number of points

Yeah, as I was explaining it to friends last night, I pretty much figured it out why it works. Then we got into a discussion about how the last cold war slide rule in Russia finally broke so they had to make this multiplication method up, and that they had just finished building a computer to comete with the WOPR from the movie War Games, etc.